A Total Correlation Evaluating User Fitting Unifac Determined from VLE Data Covering 5000 Binaries

A total correlation for VLE data covering 5000 binaries has been established, and it is applied to the consistency evaluation of binary VLE data. In particular, UNIFAC parameters were evaluated, because it is a long-standing problem for process simulator users to eliminate inaccurate VLE data predicted from built-in parameters. Furthermore, it is shown that users can fit UNIFAC parameter to the limited number of VLE data determined from the total correlation. For these purposes, high-precision lines, named TC lines [1], are used, because systematic experimental errors can be eliminated from the VLE data, if TC lines are used.

The TC lines relate X versus Y and X versus Z, in which X, Y and Z are defined as follows [2]:

X = (p1s + p2s)/(Pc1 + p2s)                                   (1)

Y =(p1sG1inf – p2s)/(Pc1 –p2s)                               (2)

Z = (p1s – p2sG2inf)/(Pc1-p2s)                               (3)

where X denotes the proximity ration to the critical point, while Y and Z denote non-dimensional infinite dilution pressure gradients at x1=1 and 0, respectively. In Eqs (1) to (3), p1s, p2s, Pc1 denote the vapor pressures of pure liquid 1 and 2, and the critical pressure of lighter component 1, respectively; G1inf and G2inf denote the infinite dilution activity coefficients of component 1 and 2, respectively; x1 denotes the liquid phase mole fraction of component 1. The G1inf and G2inf values are determined from P, x and T, x VLE data using the best correlating activity coefficient equations.

Unreliable VLE data can satisfy the Gibbs-Duhem equation. Therefore, conventional data consistency tests, such as point and area tests, cannot remove unreliable VLE data. Meanwhile, it has been shown elsewhere [3] that systematic experimental errors have substantially been eliminated from the TC lines. VLE data reported by different researchers using different methods and equipment converge to the same TC line, which show the TC line does not include experimental errors. Constant-pressure data and constant-temperature data converge to the same TC line. It should be stressed that temperature dependency of infinite dilution activity coefficients can be accurately determined from the converged X vs. Y and X vs. Z TC lines, which means that partial molar excess enthalpies and entropies can be determined. Therefore, the strength of molecular interactions and the order of molecular orientation in the liquid mixture can be estimated from the partial molar excess quantities, which will be needed in the material development procedures. Furthermore, accurate partial molar excess quantities enable us to predict reliable liquid mixture enthalpies, which is useful for the establishment of model predictive control for distillation towers.

Using TC lines, a total correlation representing VLE data covering 5000 binaries has been established [4]. First, those binaries satisfying N>6, ARDY < 0.2 and ARDZ < 0.2 were selected from the 5000 binaries, where N, ARDY and ARDZ denote the number of VLE datasets reported in the literature for a binary, average relative deviations for the X vs. Y and X vs. Z TC lines, respectively. The number of binaries satisfying the three requirements was 160. The TC lines of the 160 binaries are accurate, because convergences, i.e., ARDY and ARDZ, are high and data sources are different. Then, a variety of correlation functions has been examined for establishing a high correlation convergence of the 160 binaries. Finally, a total correlation function, J, has successfully been determined within 8 % ARD. From the x, y VLE data at 101.3 kPa of the 160 binaries, a total correlation data consistency test was established using a relative deviation from the J function value, ΔJ, as follows:

          ΔJ < 0.1               reliable VLE data

          0.1< ΔJ < 0.2     close to reliable VLE data

          0.2< ΔJ               unreliable VLE data

The total correlation data consistency test satisfactorily works, if applied to the TC line data except for the 160 binaries. Of the 5000 binaries, 5 %, 3 %, 92 % are unreliable, close and reliable VLE data, respectively.

The total correlation data consistency test was used for the evaluation of UNIFAC parameters [5]. First, from the original UNIFAC, infinite dilution activity coefficients were calculated for 23 binaries including water, alcohols, ketones, aldehydes, amines, and hydrocarbons. Next, x, y relationships of the 23 binaries were determined. Then, the x, y data were compared with these determined from TC lines, which were evaluated using the total correlation. To improve the group interaction parameters of the original UNIFAC [4], first, binaries including the groups to be improved are identified. Next, a few binaries including the same groups are chosen, if they satisfy the total correlation. Then, a part of the interaction parameters are fitted using the infinite dilution activity coefficients of the chosen binaries. The user-fitting UNIFAC is advantageous, because it can be applied for predicting VLE, in which literature data are not available. It must be stressed that the binary VLE data used for the fitting do not include experimental errors. Therefore, user can choose a limited number of binaries instead of more than 10,000 binaries used in the determination of the parameters of conventional UNIFUAC.

References

[1] Patent: US20140288905A1, EP276218A1, KR20140079425A, CN103906553A, WO2013047494A1.

[2] Satoru Kato, Juergen P. Schmelzer, Peter Gostomski, Kenneth N. Marsh, J. Chem. eng. Data, 56 (2011) 4927-4934.

[3] Satoru Kato, Peter Gostomski, Akiyoshi Oda, Joerg Freitag, Seiya Hirohama, David Bluck, Fluid Phase Equilib., 357 (2013) 36-42.

[4] http://tc-lines.com

[5] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, 1987.