The total number of experimental data points is N. Data points 1 through L and L+1 through M refer to VLB measurements (P, T, [Pg.68]

Compilation of binary experimental data reduced with the Wilson equation and, for high pressures, with a modified Redlich-Kwong equation. [Pg.9]

Characteristics are the experimental data necessary for calculating the physical properties of pure components and their mixtures. We shall distinguish several categories [Pg.86]

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. [Pg.102]

Predictions for the other isobaric systems (experimental data of Sinor, Steinhauser, and Nagata) show good agreement. Excellent agreement is obtained for the system carbon tetrachlor-ide-methanol-benzene, where the binary data are of superior quality. [Pg.55]

In typical situations, we do not have the necessary experimental data to find constants b... To obtain these constants, we need experimental vapor-liquid equilibria (i.e. activity coefficients) as a function of temperature. [Pg.88]

The viscosity coefficient fjP can also be derived from experimental data. [Pg.143]

H. The next cards provide estimates of the standard deviations of the experimental data. At least one card is needed with non-zero values. Units are the same as those of the VLE data. FORMAT(4f10.2,I2). [Pg.227]

The sampling precision of the measured data depends on the signal amplitude. The difference between simulated and experimental data can be mainly explained by the low numerical precision of the measured data. [Pg.143]

The accuracy of the calculations depends directly on the reliability of the experimental data. The correlated data presented in the Appendices were taken from standard literature sources while these data are probably reliable for most fluids, it is not possible to be certain that they are reliable for all. [Pg.95]

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. [Pg.5]

Numerical Modeling of eddy current steam generator inspection Comparison with experimental data, P.O. Gros, Review of Progress in Quantitative Nondestructive Evaluation, Vol 16 A, D.O. Thompson D. Chimenti, Eds (Plenium, New York 1997) pp 257-261. [Pg.147]

It is important to be consistent in the use of fugacity coefficients. When reducing experimental data to obtain activity coefficients, a particular method for calculating fugacity coefficients must be adopted. That same method must be employed when activity-coefficient correlations are used to generate vapor-liquid equilibria. [Pg.27]

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone. |

In spite of considerable development of thermodynamics and molecular theory, most of the methods used today are empirical and their operation requires knowledge of experimental values. However, the rate of accumulation of experimental data seems to be slowing down even though the need for precise values is on the rise. It is then necessary to rely on methods said to be predictive and which are only estimates. [Pg.85]

The contact fatigue creates independent part of the fatigue tests. As consequence of triaxial state of stress and flexible plastic state in contact area occurrence comes to very considerable scattering of experimental data. From this reason it is necessary to test statistic meaningful number of samples. [Pg.61]

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. [Pg.44]

The maximum-likelihood method, like any statistical tool, is useful for correlating and critically examining experimental information. However, it can never be a substitute for that information. While a statistical tool is useful for minimizing the required experimental effort, reliable calculated phase equilibria can only be obtained if at least some pertinent and reliable experimental data are at hand. [Pg.108]

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. [Pg.120]

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). [Pg.97]

Eddy-current non-destructive evaluation is widely used in the aerospace and nuclear power industries for the detection and characterisation of defects in metal components. The ability to predict the probe response to various types of defect is highly valuable since it enables the influence of particular parameters to be studied without recourse to costly and time consuming experiments. The solution of forward problems is also essential in the process of inverting experimental data. [Pg.140]

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1 [Pg.58]

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the [Pg.61]

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