An application of the Error-in-Variables Model—parameter estimation from Van Ness-type vapour-liquid equilibrium experiments

• Published in: Chemical engineering science 1987, Vol.42 (3), p.403-412
• Main Authors: Duever, T.A., Keeler, S.E., Reilly, P.M., Vera, J.H., Williams, P.A.
• Format: Article
• Language: English
• Subjects: Chemistry; Exact sciences and technology; General and physical chemistry; Liquid-liquid equilibria; Liquid-solid equilibria; Liquid-vapor equilibria; Others (including liquid-liquid-vapor equilibria); Phase equilibria
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/0009-2509(87)80002-7

The Error-in-Variables Model (EVM) provides a means for estimating parameter values in mathematical models where there is error in every measured variable. This is a distinct improvement over the Method of Least Squares in most situations because the latter requires that there be error in measuring only one of the variables. As an example of the use of EVM, a method is presented for estimating Wilson equation parameters in binary and ternary vapour-liquid equilibrium where the data are obtained using the Van Ness experimental technique. The application presents unusual difficulties in that the compositions of the phases are not measured directly and the total quantity of one component is only measured as the sum of a series of increments. Data for the ternary system n-heptane/ n-propanol/1-chlorobutane and the binary system n-heptane/1-chlorobutane are analysed by the proposed method, and the results are compared with the empirical results of Sayegh et al. (1979). The results of the EVM analysis are considerably more accurate. Analysis of the residuals obtained by the EVM procedure suggest serious deficiencies in the thermodynamic model.