A new method for optimizing the structure of thermodynamic correlation equations

Abstract

An optimization strategy is presented for optimizing the structure of empirical thermodynamic correlation equations. Based on a comprehensive functional expression for the physical dependence considered, which is called a “bank of terms,” the new procedure optimizes the structure and the length of the equation as well. The application of this method results in an equation which meets the quality wanted for representing the experimental data with the lowest number of fitted coefficients. The procedure can be used for the determination of the structure of any equation where the method of the linear least squares is applicable. A detailed description of the algorithm is given which includes values for the control parameters for different applications in the field of thermodynamics (vapor pressure equations, equations of state, etc.) and also for applications in other fields. The optimization steps are described using an equation which represents a relationship between variables in a general form. It is demonstrated how even the complex problem of the optimization of a fundamental equation for the Heimholtz energy can be written in terms of this general equation.