Optimum Correlations

If the pressure level is fixed to / = 30 bar, an optimization toward maximum syngas yield Tsyngas could be considered. Hence, the process temperature 9 in °C 

Maximum syngas yield syngas for p = 30 bar at variable temperature S in °C  

For p = 30 bar, the maximum cold gas efficiency //cge and the according operating parameters can be calculated depending only on temperature 9 in °C as follows. 

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Fig. 4 illustrates the time-dependence of the length of top s water column in conical capillary of the dimensions R = 15 pm and lo =310 pm at temperature T = 22°C. Experimental data for the top s column are approximated by the formula (11). The value of A is selected under the requirement to ensure optimum correlation between experimental and theoretical data. It gives Ae =3,810 J. One can see that there is satisfactory correlation between experimental and theoretical dependencies. Moreover, the value Ae has the same order of magnitude as Hamaker constant Ah. But just Ah describes one of the main components of disjoining pressure IT [13]. It confirms the rightness of our physical arguments, described above, to explain the mechanism of two-side liquid penetration into dead-end capillaries. 

In order to obtain information on the best Cl space we have carried out a systematic search with a different number of configurations on the helium atom using a STO triple zeta quality basis set. The results are given in Table IX and show that the best convergence with optimum correlation... 

The correlation between cocaine levels in the hair of mothers and their babies was investigated with 60 mother/baby pairs. All mothers had used crack cocaine during pregnancy. Hair that grew during the last trimester was used for this correlation. All mothers who reported cocaine use were found to have cocaine in their hair. For optimum correlation (r = 0.67) between drug levels in the hair of the mothers vs. that in the hair of their babies, it was necessary to exclude hair that was cosmetically treated from the comparison. 

Optimum Correlation Equations. Table XI gives the final best-fit Hansch relationships which mathematically describe the pre-emergence herbicidal activity of the 3- and 4-substituted TFMS compounds under all conditions examined in this study. The results and conclusions reached... 

Referring to Equation 4b, it is evident that there is a statistically significant parabolic relationship between apara and x for the 4-substituted TFMS derivatives. Both x2 and x terms are necessary in the optimum correlation equation, as evidenced by the fact that the percent correlation (r2) jumps from 2% in Equation 4a to 90% in Equation 4b upon stepwise addition of the linear term in x- No simple linear correlation between apara and x was found. Fits of the form o-para = f°r ex ... 

As was true for statistically significant linear relationship between (Tmeta and x was found. Quadratic relationships for o-meta similar in form to the relationships of Equations 4a and 4b are presented in Equations 5a and 5b for the meta-substituted TFMS derivatives. Both X2 and x terms are again necessary for optimum correlation although the final correlation relationship in Equation 5b for o-meta is not nearly as statistically significant (r2 = 0.44) as the final relationship for [Pg.263]

Assuming that the correction with the feedstock properties includes all the differences between the pilot and commercial unit, and that each commercial unit has the optimum correction equations with the feedstock properties, pilot test results obtained at a liquid mass velocity of above 70 Ibs/ft hr and commercial results were corrected with the feedstock properties to get the optimum correlation between two. 

The hemispherical dome (HD) test provides more reproducibility of results than the Olsen and Erichsen cup tests. For low-carbon steels, the dome height, which is determined at the point of maximum load, increases linearly with the n value. For other materials such as brass, aluminum alloys, and zinc, optimum correlation has been found between the dome height and the total elongation, which includes the effects of strain rate hardening and limiting strains. 

The development of an accurate property formulation requires analysis of the available data and correlation with a suitable functional form. The process of determining the optimum correlation often involves considerable judgment in addition to more objective protocols, and experience plays a significant part in the determination of the final result. The objective of the correlator is to ascertain the uncertainty of the available experimental data for the particular fluid or system under investigation, and to develop a mathematical model capable of representing the data within the reported or estimated experimental uncertainty. The practical models of today are empirical or semi-empirical in nature, although virtually all are based upon sound theoretical principles. The limitations of the model selected must be mutually understood by the correlator and the user for effective system optimization and related work. 

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