Development of Single Insertion Probability for Equation of State Applicable to Three Phases of Matter

A Modified Solid-Liquid-Gas Phase Equation of State

The solid-liquid-gas equation of state (SLV-EOS) is based on the initial cubic equation of state, the van der Waals equation. Since the van der Waals equation is not accurate enough to predict gas-liquid properties, SLV-EOS cannot better predict the gas-liquid properties of hydrocarbons in actual gas reservoirs. Therefore, a modified solid-liquid-gas unified equation of state was constructed inthis paper, which was developed using the material's actual critical compressibility factor Z c. The minimum liquid-phase volume at the triple point is also introduced to limit the value of c in the equation, which effectively avoids the solution of Maxwell's equal-area rule in the solid-liquid transformation process. The model extends the classical Peng-Robinson equation of state for fluid-only (liquid and vapor) states. The predicted p-T and p-ρ phase transition diagrams are reported in this paper for methane, ethane, propane, carbon dioxide, hydrogen sulfide, and sulfur, and they are in good agreement with the experimental data. This methodology is suitable for any substance for which the density of the solid phase is higher than that of the liquid phase. Additionally, the modified SLV equation can be used to estimate the solubility of solid sulfur in the absence of relevant experimental data.