A Modified Solid–Liquid–Gas Phase Equation of State

Abstract

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.

Some Features of the Modified Solid-Liquid-Vapor Equation of State

“…Therefore the expressions ( 4) and ( 8) are correct for real computations. Graphics of the expressions (4), (5) and expressions ( 8), (9) for methane are given on the fig. 2 and 3 respectively.…”

“…In the work [9] another similar equation of state has been investigated. This equation has been named the Modified Solid-Liquid-Vapor equation of state (MSLV EoS).…”

“…In this paper, we apply differential geometry to describe the thermodynamics set by the Modified Solid-Liquid-Vapor equation of state [9]. The results of our study are shown for methane.…”

“…Blue line is t 1 (4), orange -t 2 (5) Figure3:√ T for the methane phase transition at v 1 = 1. Blue line is τ 1 (8), orangeτ 2(9)…”

Equation of state for solid-liquid-vapor coexistence for heavy n-alkane

“…In the literature there are also reported other equations of state, which were developed to predict the solid phase, and all of them are non-cubic EOS. Yokozeki [7][8][9][10] introduce a discontinuity between the solid and the liquid region to avoid the solid-liquid critical point, but Lee [11,12] pointed out that the EOS has a mathematical problem because there are two singularities and suggests that Yokozeki's model should be carefully reevaluated as was recently done by Chaoping Mo, et al, [13]. Wenzel [14] modified the Peng-Robinson EoS [15] by adding a new repulsion term (like the third term in Eq.…”