Analysis and HETP Plots

Moment analysis and HETP plots were already described in Chapter 2. Here, it will be shown how they can be used in estimating the model parameters. If the detector signal is a linear function of concentration, analysis can be carried out directly with the detector signals without calibration. Since the concentration profiles are 

The signal quality (=low detector noise) and sampling rate should be sufficiently high to obtain correct results, else postprocessing of the data is necessary, such as smoothing, baseline correction, and so on. Even then the result of the integration in Equation 6.128 depends very much on the extension of the baseline, and the obtained value of the second moment can be very inaccurate (Section 6.5.3.3). 

As the parameters for the injector in Equation 6.129 are known, the plant characteristics can be calculated from the experimentally determined values of p.t,piant+inj 

If axial dispersion in the piping can be neglected. Equations 6.129-6.133 allow all plant parameters to be determined from one experiment only. Plant characterization is further discussed in Section 6.5.5. 

Experimental determination of the first and second moments of column elution profiles is straightforward, using a pulse injection with and without the column and the parameters previously determined  

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The following general methods are appropriate for the evaluation of model parameters Moment analysis and HETP plots, peak fitting and parameter estimation. They extract the information given by measured chromatograms to differing extents, which correspond to the reliability of the calculated values. 

The following methods are useful and required for the evaluation of model parameters moment analysis, HETP plots, and peak fltting. 

Figure 14.4 Comparison between plots of the HETP (cm) and of the SLT (cm) versus the mobile phase flow velocity. Same experimental conditions for both figures 5 cm long Vydac column. Mobile phase 50 50 methanol-water, monitored at 270 nm for both series of measurements. Sample 2-phenylethanol (fcg = 0.88). Height of the concentration step in frontal analysis 20 mg/mL. Sample size for linear elution peaks 40 fig (0.2 fiL of a 20 mg/mL solution). Top Figure Plot of the SLT versus the mobile phase flow velocity. Experimental data (symbols) and prediction of Eq. 14.33c (solid line). Bottom Figure Plot of the HETP versus the mobile phase velocity under linear conditions. Experimental data (symbols) and best fit to the Van Deemter equation (solid line). Reproduced with permission from /. Zhu and G. Guiochon, J. Chromatogr., 636 (1993) 189 (Fig. 2).

The major difficulty in the analysis of chromatographic data is separating the axial dispersion and mass-transfer contributions since, except for gaseous systems at very low flow rates, the axial dispersion coefficient (Dl) is velocity dependent. For liquid systems Dl varies essentially linearly with velocity so a plot of HETP vs. superficial velocity (ev) should be linear with the mass-transfer resistance directly related to the slope (Fig. 6). For gaseous systems at a high Reynolds number this same plot can be used, but in the low Reynolds number region a plot oiH/v vs. 1 /v may be more convenient since in this region Dl is essentially constant and the intercept thus yields the mass-transfer resistance [43-45]. 

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