Estimating a Stoichiometric Solid’s Gibbs Free Energy Model by Means of a Constrained Evolutionary Strategy

Abstract

Modeling of thermodynamic properties, like heat capacities for stoichiometric solids, includes the treatment of different sources of data which may be inconsistent and diverse. In this work, an approach based on the covariance matrix adaptation evolution strategy (CMA-ES) is proposed and described as an alternative method for data treatment and fitting with the support of data source dependent weight factors and physical constraints. This is applied to a Gibb’s Free Energy stoichiometric model for different magnesium sulfate hydrates by means of the NASA9 polynomial. Its behavior is proved by: (i) The comparison of the model to other standard methods for different heat capacity data, yielding a more plausible curve at high temperature ranges; (ii) the comparison of the fitted heat capacity values of MgSO4·7H2O against DSC measurements, resulting in a mean relative error of a 0.7% and a normalized root mean square deviation of 1.1%; and (iii) comparing the Van’t Hoff and proposed Stoichiometric model vapor-solid equilibrium curves to different literature data for MgSO4·7H2O, MgSO4·6H2O, and MgSO4·1H2O, resulting in similar equilibrium values, especially for MgSO4·7H2O and MgSO4·6H2O. The results show good agreement with the employed data and confirm this method as a viable alternative for fitting complex physically constrained data sets, while being a potential approach for automatic data fitting of substance data.

Residual Entropy Scaling for Long-Chain Linear Alkanes and Isomers of Alkanes

“…This means, experimental data have been excluded from the fit if the state point at which the viscosity is given is out of the range of validity of the equation of state, if the equation of state predicts the viscosity in a different phase as given by the experimental data point, and if the experimental viscosity deviates more than 30% from a preliminary model. For fitting, a modification of the algorithm described by Grau Turuelo et al 462 has been used, which utilizes the covariance matrix evolutionary strategy by Hansen and Ostermeier 463 as implemented in the DEAP evolutionary computational framework freely available for the programming language python. 464 Multiparameter equations of state, the PR, and the LKP have been used to refit the fluid-specific scaling factors ξ of eq 10 when using the global parameters listed in Table 1.…”