Experimental data, model

Models have been formulated to enable the simulation of the concentration vs. radial distance profile as it develops with time, from which the time-dependent concentration vs. distance, d, profile, observed at the probe, can be extracted for comparison with experimental data. Models based on Eqs. (29) and (30) give similar results for conditions encountered practically. 

The esterification of TPA with EG is a reaction between two bifunctional molecules which leads to a number of reactions occurring simultaneously. To simplify the evaluation of experimental data, model compounds have been used for kinetic and thermodynamic investigations [18-21], Reimschuessel and coworkers studied esterification by using EG with benzoic acid and TPA with 2-(2-methoxyethoxy) ethanol as model systems [19-21], The data for the temperature dependency of the equilibrium constants, AT, = K,(T), given in the original publications are affected by printing errors. The corrected equations are summarized in Table 2.3. 

Fig. 9.9. Film mass increment during one cycle. Comparison of modeling results (dashed line) with the experimental data. Modeling conditions correspond to experimental conditions in Ref. [93].

This switch doesn t influence on diagram of J. The advantages are the low number of parameters (they can be estimated using a little experimental data). Model curves satisfactorily approximate the experimental data if distribution is taken into account. Also we bear in mind that the algorithms of parameter identification are locally convergent. The parameter estimations of simple models should be taken as the initial approximation for more complex models. 

Figure 7. Kinetic expression of coke removal by hydrogen, experimental data model —.

The section above gives an overview of the experiments necessary to determine the model parameters. This section describes general procedures for evaluating parameter values from experimental data. Model parameters are defined in Chapter 2, while... 

Figure 3.26 Isotherm of phenyldodecane on porous graphitized carbon. Column 150 X 4.6 mm mobile phase acetonitrile, 1 mL/min. Inset plot of q/C versus C. Symbols, experimental data —, model fit. Reproduced with permission from M. Diackand G. Guiochon, Anal. Chem., 63 (1991) 2608 (Fig. 2), (c)1991 American Chemical Society.

Some of the experimental data modeled in this chapter were obtained from the literature and the experimental methods are reported therein. In all cases, sodium nitrate was used as the background electrolyte. The Co(II) adsorption data were collected by Katz and Hayes (1995a,b). Macroscopic and XAS sorption data forCd(II) were collected previously by Honcymanf 1984) ami Papeliset al. (1995), respectively. The spectroscopic data from Papelis et al. (1995) were collected on... 

The previous section gives an overview of the experiments necessary to determine the model parameters. This section describes general procedures for evaluating parameter values from experimental data. Model parameters are deflned in Chapter 2, while Section 6.2 shows how they appear in the model equations. Based on the assumptions for these models it follows that all plant effects as well as axial dispersion, void fraction, and mass transfer resistance are independent of the adsorption/desorption processes occurring within the column. 

Models that ignore axial gradients are further removed from reality and are likely to require eorrec-tion faetors (e.g., Ouyang et al., 1993) to fit experimental data. Models that account for axial variations in hydrodynamic variables have found a variety of ways of doing so, e.g.. 

Fig. 19 Enhancement of oxygen mass tramsfer in aqueous solution by small droplets of hexadecane vol % hexadecame experimental data — model prediction From Bruining et al. [146]...

In 1972, Lakshmana Rao and his co-workers obtained the pressure loss coefficients for laminar flow in five sharp square-edged long orifices with a constant p ratio of 0.2 whilst varying the thickness to diameter ratios from 0.48 to 10.11. Pressure loss coefficients in turbulent flow for orifices with P ratios of 0.36, 0.4, 0.5 and 0.7 with aspect ratios of 4, 4, 5 and 5 respectively are compared with those of Ward-Smith (1971) and Idel chik et al. (1994). Excellent agreement was found between experimental work and turbulent flow correlations from Ward-Smith (1971) and Idel chik et al. (1994), with maximum difference between the experimental data models were 9.87% and 12% respectively for the maximum beta ratio of 0.7. This difference was well within the experimental error obtained. The comparison shows clearly that correlations published by Ward-Smith (1971) and Idel chik et al. (1994) can be used from Re > 1000, although the two models has an applicability range from Re > ICh. 

FIG. 10 Residence time distribution ( ) experimental data (—) model prediction. 

S-4.4.2 Multiphase Model. Both solids suspension and gas sparging can be simulated using an experimental data model for the impeller. The manner in which the multiphase parameters are input depends on the multiphase model being used. For solids suspension, an Eulerian granular multiphase model is recommended, and separate sets of momentum equations are used for the liquid and solids phases. This model, run in a time-dependent fashion, is fully compatible with the time-averaged representation of the impellers. Experimental velocity data are set as a boundary condition independently for each of the phases. Note,... 

Fig. 4-5. Generalized composite model calculations of U(VI) adsorption by the Koongarra W1 sample equilibrated with air compared with experimental data. Model 1 calibrated to all Koongarra schist adsorption data in the pH range from 4 to 10. Model 2 calibrated to Koongarra schist adsorption data in the pH range from 6 to 8.6 for systems equilibrated with air. Model 3 calibrated to Koongarra schist adsorption data in the pH range from 6 to 8.6 for systems equilibrated with air and 1 % CO2.

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