Vapor Pressure Fitting Techniques and Correlations within Multi-Property Optimization
Hogge, J.; Knotts,T.; Giles, N.; Rowley, R.; Wilding, W.
Pure component vapor pressure is one of the most important thermodynamic properties used in chemical engineering design. It may be used directly (e.g. phase equilibrium calculations) or indirectly when used to predict other thermodynamic properties (e.g. determining heats of vaporization from the Clapeyron relationship). Because this property is temperature dependent, the experimental data are usually reduced through fitting to facilitate easy tabulation in reference texts and for use in simulation software.
Several fitting methods and temperature dependent correlations may be used in the data reduction process. Most perform very well in that they reproduce the experimental data values, but recent work in our group has shown that the technique employed can significantly affect the slope of the vapor pressure curve. This is especially problematic when the derivative of vapor pressure is used in relationships with other thermodynamic properties.
This paper will discuss how the fitting method affects the slopes of the vapor pressure curve. Specifically, two different methods will be considered. The first, which is most common due to its computational tractability, is fitting the natural logarithm of the vapor pressure data to a linear correlation form by inverting the coefficient matrix. The second requires nonlinear regression through minimization of the sum of the squared errors between the data and the correlation and requires selection of an error model. In this presentation, we show tests of the fitting methods using the Riedel and Wagner expressions for vapor pressure for several well-known compounds. We focus on the ability of the resulting expressions to predict the heat of vaporization and liquid heat capacity using rigorous, thermodynamic relationships involving the vapor pressure. These thermodynamic relationships include the Clapeyron equation and the temperature derivative of the heat of vaporization.
Finally, due to the interconnectedness of these properties, we show how fitting sets of rigorously-related data simultaneously results in better consistency among the related properties and a more accurate thermodynamic picture of the compound. This multi-property optimization uses vapor pressure, heat of vaporization, liquid isobaric heat capacity, and ideal gas isobaric heat capacity experimental data with the thermodynamic relationships to find the best fit. The performance of this optimization method is given by comparing the resulting correlations for each property with experimental data for several compounds. Taken as a whole, the results show that combining proper fitting techniques with simultaneous fitting of related properties greatly improves our ability to both interpolate and extrapolate available data.