(449b) Symbolic Regression of Alpha Functions for Cubic Equations of State

Since Van der Waal first proposed a formulation for a thermodynamic cubic equation of state, modifications to the thermodynamic cubic equations of state have focused on the alpha function of the attraction term to model the temperature dependence of attraction for real fluids [1]. The alpha function is dependent on reduced temperature and density and acentric factor. Modifications to Peng Robinson and Redlich-Kwong forms of the cubic equation have focused on the functional form of the alpha function fit prior to fitting the attraction and repulsion values for the cubic equation. Traditionally, cubic equations are derived from the critical point which leads to errors in liquid density and in the critical region. Alternatively, when fit to chemical-specific liquid density and vapor pressure data, the equations fail to represent the critical constraints [2].

To improve the development of cubic equations and their regression, we focus on a data-driven constrained symbolic regression to simultaneously determine the model form of the alpha function and fit parameters of the cubic equation. Symbolic regression learns both the model structure and parameters to model a data set, unlike traditional regression that limits the scope of the regression to a fixed functional form [4]. The regression only requires the specification of a set of operators and operands (+, -, *,÷, exp(·), log(·), (·)², (·)³, √·, etc.) to flexibly develop new functional forms that accurately represent the data. Symbolic regression has typically been performed with genetic programming [4], but recent developments in applying global deterministic approach have shown improved fitting metrics, such as sum of squared error and other information criteria [3]. We use this approach to apply symbolic regression to pure fluids to determine new alpha function forms for cubic equations of state and compare their accuracy to the data, specifically in liquid density and supercritical regions, and adherence to theoretical thermodynamic properties with other alpha modifications of cubic equations of state.

Reference cited:

[1] Valderrama, J. O. The State of the Cubic Equations of State. Ind. Eng. Chem. Res. 2003, 42, 1603-1618.

[2] Twu, C.H. & Sim, W.D. & Tassone, V. (2002). Getting a Handle on Advanced Cubic Equations of State. Chemical Engineering Progress. 98. 58-65.

[3] Cozad, A. & Sahinidis, N.V. (2018). A global MINLP approach to symbolic regression. Mathematical Programming, to appear.

[4] J. R. Koza. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, 1992.