Comparison of Strategies for the Development of a Helmholtz Equation of State for Solid Benzene I

The calculation of thermodynamic properties is important for the operation of many technical applications. For example, the liquefied natural gas (LNG) industry requires accurate knowledge about the solubility of the single components in the LNG mixture, e.g., benzene, to prevent solids freeze-out, blockages and ultimately LNG plant shutdowns. To incorporate the knowledge of the thermodynamic behavior in process operations, equations of state in form of the Helmholtz energy are commonly used due to their ability to predict all thermodynamic properties. Many modeling approaches heavily rely on the theoretical expertise of the developer and can be time-consuming, especially when no preexisting functional form for the model is available. In this study, a novel method for the development of thermodynamic equations of state using machine learning, specifically symbolic regression, is presented. The limited use of symbolic regression in thermodynamic property modeling is due to the absence of thermodynamic constraints. This is the main reason why a novel thermodynamics- informed symbolic regression tool called TiSR is developed in this work. To evaluate the applicability and the performance of this tool, an existing modeling approach as published by J. P. M. Trusler (J. Phys. Chem. Ref. Data 40, 043105, 2011) and adapted for solid benzene by X. Xiao et al. (J. Phys. Chem. Ref. Data 50, 043104, 2021) is compared with TiSR using solid benzene as an example, based on the identical input data. Symbolic regression generates multiple models simultaneously, allowing users to select the most suitable model based on complexity and accuracy. This study contributes to advancing machine learning techniques in thermodynamics and facilitating the development of accurate models for substances in LNG.