Analysis of the thermodynamic behavior of gaseous mixtures using equations of state

Abstract

Cubic equations of state are utilized to model the behavior of substances in both liquid and gaseous states, incorporating cubic order terms in their variables. These equations are pivotal in describing the behavior of real substances, particularly their deviations from ideal behavior. Furthermore, they facilitate the prediction of a range of thermodynamic properties, including pressure, volume, temperature, and compressibility factors. This study was conducted with the objective of evaluating the compressibility factor using four distinct cubic equations of state: Van der Waals, Redlich–Kwong, Soave-Redlich–KwongRedlich–Kwong, and Peng–Robinson. The analysis focused on the dependency of these equations on temperature, pressure, and component fractions in binary mixtures. A numerical algorithm, featuring algebraic solutions, was developed on the Excel platform to enable graphical analysis of the mixtures in question. The results of this analysis led to the establishment of a parametric relationship for the compressibility factor, dependent on temperature, pressure, and concentration.

The study's findings reveal significant discrepancies in the compressibility factors calculated using the Van der Waals (VDW) equation compared to those from the Redlich–Kwong (R–KR–K) and Peng–Robinson (P–R) equations, with deviations reaching as high as 16.13 %. Specifically, at the maximum pressure investigated, the compressibility factor derived from the VDW equation (1.519) significantly differed from that obtained via the Soave-Redlich–Kwong (S-R–K) equation (1.222), showing a 0.297 difference, or 19.55 %. This disparity is attributed to how temperature affects the repulsive forces term in the S-R–K, P–R, and R–K equations, leading to a closer approximation of the compressibility factor profile. Additionally, the P–R and S-R–K cubic state equations account for the acentric factor, a crucial parameter that influences compressibility factor behavior by considering the molecular size involved in the process. In conclusion, the Soave-Redlich–Kwong cubic equation of state was found to align most closely with experimental data and was therefore selected to explore the compressibility factor's behavior in relation to pressure across various fractions and temperatures within the examined systems.