Vapor composition, sources error

A comparison of columns 4 and 8 reveals no clear pattern, which is perhaps of greater significance. The use of raw data yields smaller values of the vapor composition sample deviations in four out of six cases, but the effects are small and could be masked by errors in the vapor compositions themselves. It seems likely that the greatest source of error lies in determination of vapor composition. Thus there is very little difference in using raw or smoothed data. A typical example of the fit is shown in Figure 2. The optimum smoothing parameters used in run 1 were found to be the same as required for run 2, and are listed in columns 11 and 12 of Table II. 

A second explanation involves the relative accuracy of the first three data points. Examination of the Ay values (Figure 3) reveals that the contribution of these three values distorts the final result. By ignoring them we can reduce the sample deviation from 0.1381 to 0.0387. The All values (Figure 4) show no particular bias hence we might conclude that a likely source of error is in the experimental vapor compositions. In practice, the attainment of true equilibrium... 

Select the criterion to be used for thermodynamic consistency. Deviations from thermodynamic consistency arise as a result of experimental errors. Impurities in the samples used for vapor-liquid equilibrium measurements are often the source of error. A complete set of vapor-liquid equilibrium data includes temperature T. pressure P. liquid composition x, and vapor composition y,. Usual practice is to convert these data into activity coefficients by the following equation, which is a rearranged form of the equation that rigorously defines K values (i.e., defines the ratio y, /x, under Related Calculations in Example 3.1) ... 

In the calculation of total pressure and vapor composition from boiling point data using the indirect method, the greatest source of error lies in the liquid-phase composition. We have attempted to characterize the frequency distribution of the error in the calculated vapor composition by the standard statistical methods and this has given a satisfactory result for the methanol- vater system saturated with sodium chloride when the following estimates of the standard deviation were used x, 0.003 y, 0.006 T, 0.1° C and tt, 2 mm Hg. This work indicates that in the design of future experiments more data points are required and, for each variable, a reliable estimate of the standard deviation is highly desirable. 

There are three sources of error in the calculated vapor composition when these are calculated from boiling point data random error in each experimental observation systematic error in one or more of the observations and the model is imperfect (this is particularly true for isobaric data because use is made of the Gibbs-Duhem equation which was derived for constant temperature and pressure). In the present work we shall assume that the only error in the data is caused by randomness. 

Table II gives the standard deviations of pressure, vapor composition and temperature, and the corresponding bias and D-value as each variable is changed randomly and then as all four are changed simultaneously. We see that the random error of x contributes ca. 75% of the induced error in the value of the standard deviation of both the pressure and temperature while the random error of T and tt only contribute about 12% each. On the other hand the random errors of x and y contribute equally to the induced-vapor composition standard deviation with the pressure making a negligible contribution. The bias values are negligibly small except for the pressure standard deviations where they are still not large. The final column has D-values at least equal to two and this gives one confidence in the model and suggests it is adequate for good quality data as in this particular case the only source of error is caused by random behavior.

Several conclusions can be drawn from this work. First, in the calculation of total pressure and vapor composition from boiling point data the greatest source of error lies in the liquid-phase composition, particularly at low concentration. Second, the estimates of the standard deviation for vapor composition and temperature of 0.006 and 0.1°C,... 

Another source of error in the system is possible because the condensate returned to the still is of a different composition from the liquid in the still and in general is of lower boiling point. If this vaporizes before it is completely mixed with all of the liquid in the still, this vapor composition will not be an equilibrium vapor. 

Care must be taken in the selection of experimental vapor/liquid equilibrium data used in the calculations. These data should cover the range of compositions proposed for the column being designed. Extrapolation of VLE data, especially into high purity areas, can be a source of significant errors. 

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