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Solid formation and deposition in liquefied natural gas (LNG) production is a process hazard avoidable by careful determination of impurity solubility in the process stream. Accurate freeze-out predictions for LNG require robust thermodynamic models tuned to high-quality experimental data. Cubic equations of state (EoS) can be used to calculate solid–fluid equilibria (SFE) for LNG-relevant binary mixtures with the necessary accuracy, while retaining the computational efficiency ideal for process simulations. A comprehensive literature survey of the available experimental SFE data of LNG-relevant binary mixtures was carried out and used to determine the optimal binary interaction parameters for a range of commonly-used cubic EoS. Overall, the Peng-Robinson (PR) EoS performed best representing the SFE temperatures with a standard uncertainty of less than 2 K for most of the examined mixtures; the Soave-Redlich-Kwong (SRK), Peng-Robinson-Stryjek-Vera (PRSV) and Patel-Teja-Valderrama (PTV) equations produced similar results. The solubility of various impurities in methane was investigated with the optimized EoS across a range of temperatures, and various retrograde behaviors were examined. The EoS models and the best-fit parameters obtained in this work have been incorporated into the ThermoFAST desktop application and a new free online implementation ThermoFAST Web.