Consistency of VLE data

Clausius/Clapeyron equation, 182 Coefficient of performance, 275-279, 282-283 Combustion, standard heat of, 123 Compressibility, isothermal, 58-59, 171-172 Compressibility factor, 62-63, 176 generalized correlations for, 85-96 for mixtures, 471-472, 476-477 Compression, in flow processes, 234-241 Conservation of energy, 12-17, 212-217 (See also First law of thermodynamics) Consistency, of VLE data, 355-357 Continuity equation, 211 Control volume, 210-211, 548-550 Conversion factors, table of, 570 Corresponding states correlations, 87-92, 189-199, 334-343 theorem of, 86... 

There is also an accurate four-suffix formula that may be employed to test the thermodynamic consistency of VLE data. 

In the case of isothermal or isobaric data one term in the equation above can be cancelled. Since the pressure dependence can usually be neglected, in the case of isothermal VLE data the following simple relation can be used for checking the thermodynamic consistency of VLE data ... 

For limitations of the area test and other techniques of testing the consistency of VLE data see Prausnitz et al, 1986. 

Worth noting is the fact that Barker s method does not require experimental j/f values. Thus the correlating parameters a, P, and so on, can be evaluated from a P-Xi data subset. Common practice now is, in fact, to measure just such data. They are, of course, not subject to a test for consistency by the Gibbs/Duhem equation. The world s store of VLE data has been compiled by Gmehhng et al. Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol. I, parts 1-8, DECHEMA, Frankfurt am Main, 1979-1990). 

Thus, from the VLE diagram of a binary mixture one can see at a glance whether the fractional separation is going to be easy or not. A huge collection of VLE data has been made by Dechema currently consisting of about 17 volumes, which are all available at the Scientific Research and Information Service (SRIS) library in London. 

Binary systems with only two degrees of freedom can be conveniently represented in tabular or graphical form by setting one variable (usually pressure) constant. VLE data have been determined for many binary systems. Sources for these data are listed in Table 2-2 you should become familiar with several of these sources. Note that the data are not of equal quality. Methods for testing the thermodynamic consistency of equilibrium data are discussed in detail by Barnicki (2Q02), Walas (1985), and Van Ness and Abbott (1982, pp. 56-64, 301-348). Errors in the equilibrium data can have a profound effect on the design of the separation method (e.g., see Carlson. 1996. or Nelson etal.. 1983V... 

In practice almost exclusively VLE data are used to fit the required parameters. Since a distillation column works nearly at constant pressure, most chemical engineers prefer thermodynamically consistent isobaric VLE-data in contrast to isothermal VLE-data to fit the model parameters. But that can cause problems, in particular if the boiling points of the two compounds considered are very different [24], as for example, for the binary system ethanol-n-decane. The result of the Wilson equation after fitting temperature-independent binary parameters only to reliable isobaric data at 1 atm is shown in Figure 5.31 for the system ethanol-n-decane, where the sum of the relative deviations of the activity coefficients was used as objective function. 

Figure 5.31 Result of the fit of temperature-independent Wilson parameters to consistent isobaric VLE data at 1 atm of the system ethanol (l)-n-decano (2) and calculated results for the excess enthalpies and activity coefficients at infinite dilution for...

Then of course the data used should be distributed equally over the whole temperature (pressure) range Since often a lot of VLE data at atmospheric pressure are reported, perhaps some of the data have to be removed or at least a lower weighting factor for the numerous data should be used. The same is true for excess enthalpies. Most authors have measured excess enthalpies around room temperature. For fitting temperature-dependent model parameters the whole temperature range should be covered. While consistent VLE data (azeotropic data) provide the information about the composition... 

The progress achieved when going from UNIFAC to modified UNIFAC can be recognized from a comparison of the results for 2200 consistent binary VLE data sets. Using the UNIQUAC equation for the correlation of the 2200 VLE data sets... 

Data for the hydrogen sulfide-water and the methane-n-hexane binary systems were considered. The first is a type III system in the binary phase diagram classification scheme of van Konynenburg and Scott. Experimental data from Selleck et al. (1952) were used. Carroll and Mather (1989a b) presented a new interpretation of these data and also new three phase data. In this work, only those VLE data from Selleck et al. (1952) that are consistent with the new data were used. Data for the methane-n-hexane system are available from Poston and McKetta (1966) and Lin et al. (1977). This is a type V system. 

Several authors have attempted to correlate the vapor-liquid equilibrium (VLE) data for binary systems in the presence of salts at various concentrations. Johnson and Furter (4) successfully correlated a large number of systems consisting of an alcohol, water, and a salt at saturation, by the following equation ... 

There are no thermodynamic consistency tests that can be applied to the data. For each system in the infinite dilution VLE data base, the weight fraction activity coefficients were plotted as a function of temperature. In many cases considerable scatter was observed. Some data were found that were significantly outside the anticipated range or which showed contradictory behavior with temperature from that expected. These points were kept in the data base but are indicated by an "R", for Rejected, if they were judged to be clearly erroneous or by an "N", for Not recommended, if they appeared questionable but not obviously incorrect. Similarly, in the finite concentration VLE data base some points were judged to be significant outliers and are indicated accordingly. 

Data Quality Normally, it is not possible to evaluate LLE data for thermodynamic consistency [Sorenson and Arlt, Liquid-Liquid Equilibrium Data Collection, Binary Systems, vol. V, pt. 1 (DECHEMA, 1979), p. 12]. The thermodynamic consistency test for VLE data involves calculating an independently measured variable from the others (usually the vapor composition from the temperature, pressure, and liquid composition) and comparing the measurement with the calculated value. Since LLE data are only very weakly affected by change in pressure, this method is not feasible for LLE. However, if the data were produced by equilibration and analysis of both phases, then at least the data can be checked to determine how well the material balance closes. This can be done by plotting the total... 

We first investigated the behavior of mixtures of the normal paraffinic solvents pentane, heptane, and decane with gaseous methane. These mixtures consist of two main UNIFAC groups, methane and the main methyl group CH2 thus, there are only two binary interaction parameters to evaluate. We used the VLE data for the 377 K isotherm of the methane and n-heptane mixture to obtain these parameters for both the HVOS and LCVM models the parameter values are reported in Table 5.3.1. We then estimated the VLE at all other temperatures of the three mixtures. The results... 

Before the activity coefficients are represented with an equation, it is important to check the VLE data for thermodynamic consistency against Equation 1.30. As concluded earlier, the error introduced by applying Equation 1.30 to binary isothermal data is usually negligible. The consistency check is described for this type of data, which is the most commonly used for equation development. Equation 1.30 is written for a binary as... 

Very important for the practical determination of vapor-liquid equilibria are collections of experimental vapor-hquid-equilibrium (VLE) data. The collection of (Gmehling and Onken 197711) consists of about 20 volumes containing vapor-liquid equilibria of nearly all binary, ternary, and quaternary mixtures pirbhshed so far. A collection of azeotropic data (Gmehling et al. 2004) lists data of 18,000 systems involving approximately 1,700 compounds. 

For the system methyl acetate-acetic acid-methanol-water he determined VLE data for all six binary systems, unless thermodynamically consistent values were already available from literature, for the four ternary systems and for the quaternary system with and without the catalyst. It was found that the presence of sulphuric acid in the composition range of up to 4 wt-%, as normally encountered in homogeneous catalysis, had negligible effect on the equilibrium data calculated on acid-free basis. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

After integration from xi = 0 to xi = 1 an expression is obtained, which can be applied for the graphical examination of complete VLE data for thermodynamic consistency. 

The consistency test (Redlich-Kister test) is performed by plotting the logarithmic value of the ratio of the activity coefficients as a function of the mole fraction xi. If the VLE data are thermodynamically consistent the area above and below the x-axis should be equal. 

Figure 5.27 Check of isothermal complete VLE data of the system ethanol (l)-water (2) [8] for thermodynamic consistency v ith the help of the area test.

Often isothermal Px-data are measured (see Table 5.7). They cannot be checked for thermodynamic consistency. But if the data can be described very accurately with the help of a consistent g -model, these VLE data can also be considered as thermodynamically consistent. The same is true for other incomplete VLE data listed in Table 5.7. 

For a large number of binary systems the required binary -model parameters for the Wilson, NRTL, and UNIQUAC equation and the results of the consistency tests can be found in the VLE Data Collection of the DECHEMA Chemistry Data Series published by Gmehling et al [6]. One example page is shown in Figure 5.30. It shows the VLE data for the system ethanol and water at 70 ""C published by Mertl [8]. On every page of this data compilation the reader will find the system, the reference, the Antoine constants with the range of validity, the experimental... 

VLE data, the results of two thermodynamic consistency tests, and the parameters of different -models, such as the Wilson, NRTL, and UNIQUAC equation. Additionally, the parameters of the Margules [28] and van Laar [29] equation are listed. Furthermore, the calculated results for the different models are given. For the model which shows the lowest mean deviation in vapor phase mole fraction the results are additionally shown in graphical form together with the experimental data and the calculated activity coefficients at infinite dilution. In the appendix of the data compilation the reader will find the additionally required pure component data, such as the molar volumes for the Wilson equation, the relative van der Waals properties for the UNIQUAC equation, and the parameters of the dimerization constants for carboxylic acids. Usually, the Antoine parameter A is adjusted to A to start from the vapor pressure data given by the authors, and to use the -model parameters only to describe the deviation from Raoult s law. Since in this data compilation only VLE data up to 5000 mm Hg are presented, ideal vapor phase behavior is assumed when fitting the parameters. For systems with carboxylic acids the association model is used to describe the deviation from ideal vapor phase behavior. 

Figure 5.85 Mean absolute deviation in vapor phase mole fraction, temperature, and pressure for the correlation, respectively, prediction of 2200 binary consistent VLE data.

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