Average relative deviation

Functional and method Average (absolute) deviation Average relative deviation comment... 

In the followed tables, the average relative deviations are such as ... 

The calculation of the liquid-fluid equilibria with the group contribution method has been presented elsewhere [4], The matrix of the parameters of group interaction (Table 1) contains values readjusted relative to the matrix obtained considering only liquid-fluid equilibria [4], These parameters are Ai5, A35, A45 and A59. The introduction of supplementary increments for the form of the molecules (a3 and P3.5) enables good results to be obtained for the calculation of solid-fluid equilibria and does not essentially modify the representation of liquid-fluid equilibria. The average relative deviation 5r(x) for the experimental data as a whole is 16 7% for the group contribution method and 13.3% for the model with E12 adjusted. The experimental data concern 40 isotherms (P,x) for 11 binary mixtures of solid aromatic hydrocarbon with supercritical C02. 

In Figure 7, the respective parameters are illustrated in a graph. The isotherm model selected is explicit in C and therefore is well suited for computer simulation of the entire process. Physically meaningliil values result for the limiting cases. The average relative deviations between the measured and the calculated (for X = fimct. (C)) loading values were in between 2 and 6% for the different solvents. They were in the same order of magnitude as expected for variations caused by the adsorbent properties due to variations in production quality of the ACC. This was documented by measurement series on quality. 

Then a and By were optimized to minimize the percent absolute average relative deviation (% AARD) between the calculated solubility and the experimental solubilty measured here, and the experimental solubilities at 35 C reported by Tsekhanskaya et al. (11) and by McHugh and Paulaitis (12), The equilibrium solubilities of naphthalene in CO2 used to calculate the mass transfer coefficients are given in Table IL The optimized values of ay, By, and %AARD are 0.0402, 6.5384 and 9.23 respectively. Prediction of the solubility with these two optimized parameters is given in Figure 2 with data of Tsekhanskaya et al. (Ij, McHugh and Paulaitis (12) and our experimental solubility data (below the critical pressure). 

AARD = percent absolute average relative deviation. 

In this study, a modified Simplex method was used to regress the binary interaction parameter, fcy, using a packaged algorithm, DBCPOL (13), The objective function minimized by the optimization routine was the percent absolute average relative deviation (%AARD)... 

The fit of the target vectors in matrix L and the predicted vectors in matrix L based on the transformation matrix according to Eq. (5.77) is usually estimated by the average relative deviation as follows ... 

In Ellegaard, Abildskov, and O Connell (2010), data were analyzed from nine pharmaceutical solutes in a total of 68 binary mixtures of 10 solvents, with some of the mixtures at different temperatures. The absolute average relative deviation of using parameters from binary data was 23% while that from correlation of ternary data was 11%. Additional study of this method is described in Ellegaard (2011) with more solutes and binary solvents, as well as in some ternary solvents. Fignre 9.10 shows excess solubility results for representative systems. 

Figure 4.7 (A) Average relative deviation (in %) between two independent time-averaged vector images over a certain number of data fiies as a function of that number and (B) average relative deviation (in %) between two independent time-averaged bubble size data files as a function of the number of bubbies encountered in that series on a doubie iogarithmic scaie. Reprinted from De Jong et al. (2011) with permission from Elsevier.

Strongly depends on how many bubbles were detected at that specific height in the fluidized bed. Therefore, in Fig. 4.7B, the average relative deviation between two independent series is plotted on a log—log scale as a function of the number of bubbles that were present in the fluidized bed in those series. Again, a power trend Hne is used to provide an estimate of the experimental error as a function of the number of bubbles. It has been found that when over 100 bubbles were encountered, the statistical error reduces to below 5%. 

The comparison of the experimental data with all equations by Billet and Schultes [316, 322] using the constants presented in Table 6 shows the following average relative deviations for loading and flooding point - 5% for liquid holdup- 6.7% for pressure drop- 9.1% ... 

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