Parity Plot

Parity Plots A parity plot is used to present the overall results of an analysis visually. The parity plot is especially valuable when a complex model has been developed by piecewise analysis of various subsets of data. 

A parity plot is nothing more than a plot of the result calculated from the model (in this case, the first-order rate equation) against the experimental result. If the model were perfect and there was no error in the data, every point on a parity plot would fall on a line though the origin with a slope of 1. In reality, the data points will contain experimental error and will scatter around this line. However, if the model fits the data, the deviations will not be large, and the scatter will be random. 

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OS 41b] ]R 19] ]P 30] A Parity plot (Figure 4.65) for five different substrates (C4-Cg alcohols) was derived, showing a comparison of experimental data with a plug and laminar flow model [112]. In the plug-flow case, much higher conversions were theoretically expected than actually measured. Laminar-flow modeling describes the results much better and is in line with visual inspections of the liquid/liquid flow. 

Figure 4.65 Parity plot comparing the conversion of a batch and laminar flow model for five different substrates made by allyl alcohol isomerization. For calculation, the same rate law was used for all substrates. The increase in conversion is due to increased substrate solubility [112].

Figure 38.3. Parity plot for ninhydrin titrations showing measured amine...

FIGURE 16.7 Parity plot for calculated and experimental CO conversion. 

The parameters kco and /c,, 2 are taken to be the reaction rate constants for the reduction of surface by CO and reoxidation of it by 02. The parameters kco, k(>2, and n at one temperature were obtained by fitting the experimental values of Pco, P0l, and reaction rate with the above rate equation. The parity plot for calculated vs. experimental values of reaction rate is presented in Figure 7.13. The agreement between experimental and calculated values is very good over three orders of magnitude of reaction rate. 

Figure 5.34 Parity plot showing the quality of the rate prediction using Eq. 5.40 and experimental rate data [53]...

The quality of the A correlation from Eq. 7.56 is shown by plotting it as a function of the A determined from the numerical experiments. The quality is shown by Fig. 7.28 using a parity plot. 

Figure 7.28 Parity plot showing the quality of the F,. correlation function (Eq. 7.56) with the numerical experiments...

Figure 9.7a shows values of stable drop diameters that are calculated with Eqs. (9.3) and (9.4) for special conditions for the liquid system toluene-water as a function of the product of pulse amplitude, a, and frequency, /, the so-called pulse intensity. Figure 9.7b is a parity plot and shows that Eq. 9.4 describes the measured drop sizes for a wide range of velocities and parameters of the sieve tray geometry quite well. 

Figure 5.2-32. Parity plot of the correlation (5.2-28) to estimate the total liquid hold-up (after Larachi et al. [37]).

Figure 2.6 Parity plot of measured and experimentally determined reaction rates of methanol steam reforming [24] (by courtesy of Springer Verlag).

Figure 2.30 Parity plot based on the Langmuir-Hinshelwood kinetics of the 02 reaction rate r02 for hydrogen oxidation as determined over microstructured Pt-impregnated stainless-steel foils [61] (by courtesy of O. Gorke).

Figure 4.55 Kinetic study for the hydrogenation of a cinnamonic acid derivative parity plot comparing experimental and modeling data. Open and closed circles correspond to data outside orwithin a match of experiments and modeling (by courtesy of Elsevier) [325],...

Fig.8 Activity decline at diffe- Fig.9 Parity plot for the coke...

Solution of the shrinking core model at zero time (t=0) depends only on two parameters the solubility of solute in SC CO2 and the external particle to fluid mass transfer coefficient Kq. Hence, knowing the solubility, measurements of the initial extraction rates allow to determine the values of K(j. Detailed discussion on the evaluated mass transfer coefficients are given in [7].These authors found that the overall mass transfer from particles to fluid depends upon both free and forced convection mechanism. Figure 2 illustrates a parity plot of die experimental values of Sh number (evaluated by zero-time solution of the shrinking core model) and the calculated Sh number (using an appropriate mass transfer correlation). 

Figure 2. Comparison between a measured Figure 3. Parity plot of calculated vs. calculated with Eq. 3 and experimental data predicted kta values...

The parity plot of calculated vs. experimental results of kLa under high pressure conditions is shown in Fig. 3. Even though measured data are scattered, they constitute to our knowledge the only existing experimental values obtained in a pressurised TBR. Experimental results are reasonably well predicted from the previous analysis as can be judged from the statistical test shown in Table 3. 

The parity plot for the above equation for holdup is shown in Figure 1. While the validity of the above correlation for an electrolyte solution may be questionable due to its coalescence hindering property, at present, no conclusive data illustrating this effect, particularly for dilute NaOH solutions are available. Experiments were performed at... 

Figure 1. Parity Plot for Correlation of Small Bubble Holdup,...

Plots of data can be informative, for example parity plots and relative residual plots. Figure 2.7 shows parity plots, in which measured data are plotted against the data as cal-... 

Figure 2.7 Parity plots of measured and correlated data for the hydrogenation of (a) acetylene and (b) ethane [4]. In a parity plot the data as calculated with the correlation, and as measured experimentally, coincide with the diagonal if they are exactly equal.

Figure 7-27 A parity plot for Eq. (7-281 using the data of Alexander and Shah.2...

Figure 19 Parity plots of the NO conversion in the BSR. (a) LCR model (b) LCF model (c) CB model (d) CBS model.

To reversely check the kinetic model, the integral rate equation (for non-isothermal conditions) describing the As release during pyrolysis of CCA treated wood is used in combination with the measured temperature profiles T(t) in order to calculate the corresponding As content of the pyrolysis residues. The calculated arsenic content of the pyrolysis residues is compared with the experimental values labscale and TGA experiments) in the parity plot, presented in Figure 5. 

Fig. 5 Parity plot experimental As contents of the pyrolysis residues (o for labscale, for TG experiments) are compared with the calculated values, using the first order single reaction kinetic scheme. The errorbars represent 95 Vc confidence intervals.

In Eq. (15-135), is the specific wall surface (cmVcm ) and flp is the specific packing surface (cmvcm ). This term is dropped for a spray column (Cl = 0). The model coefficients are summarized in Table 15-19. Most of the axial mixing data available in the literature are for the continuous phase dispersed-phase axial mixing data are rare. Becker recommends assuming HDU = HDU, when dispersed-phase data are not available. Becker presents a parity plot (Fig. 15-33) based on small- and large-scale data for packed and spray columns. 

FIG. 15-33 Parity plot comparing spray and packed column results incorporating axial mixing model. [Reprinted from Becker, Chemie Ing. Technik, 74(1-2), pp. 59-66 (2002). Copyright 2002 Wiley-VCH.]... 

A parity plot comparing predicted overhead and bottoms compositions is provided in Figure 14.34. All four product compositions at both ends of the column are included in this illustration. It can be seen that the product compositions are predicted quite well. Product temperatures were predicted to within one-half a degree Celsius. 

Figure 6. Parity plots of calculated and observed mole fractions of isobutene, oxygen, carbon dioxide and DMH. T = 530°C, 550°C, 570°C, W/F = 1000 g min-mor, 2000 g-min-mol, pisobutene 2 kPa, 4 kPa, 8 kPa...

Figure 6 Power law modell Parity plots of calculated and observed mole fractions...

Except for a few points, the parity plot of benzene and nitrous oxide mole fractions displays a satisfactory agreement with a maximum deviation of 10% (Fig. 6 left). The higher deviation between calculated and measured phenol values (Fig. 6 right) stems from the simplicity of the model for the description of more complex consecutive reactions of phenol. 

With a more mechanistic model for predicting tray point efficiency, Garcia and Fair showed a better fit to a large database than did the older Chan-Fair model. A parity plot for the Garcia-Fair work is given in Figure 12.64. The newer method is more complex, however, and requires a fairly elaborate computer program. 

FIGURE 12.64 Parity plot for Garcia-Fair efficiency prediction method. (2002. Ind. Eng. Ghent. Res. 41 1632.)... 

FIGURE 13.19 Parity plot for calculated vs. measured mass transfer coefficients, air-stripping of volatile organic compounds from water with air. 

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