The Thermodynamic Analysis of a Gas Mixture Utilizing Peng-Robinson and Soave-Redlich-Kwong Cubic Equations of State

Abstract

Cubic equations of state are mathematical models used to describe the thermodynamic behavior of pure substances or mixtures of substances by calculating physical and chemical properties under different pressure and temperature conditions. These equations are widely employed in various scientific fields, particularly in chemical engineering, for the thermodynamic study of physical and chemical processes involving phase equilibrium. Thus, the knowledge derived from these studies enables the development of industrial processes, the synthesis of new processes and materials, the study of chemical reaction kinetics, analysis of experimental data, and more. Therefore, this study aims to describe deviations from ideality in real gases, evaluated based on the behavior of the compressibility factor (Z) as a function of pressure (P) for a binary mixture involving hydrogen (H2) and carbon dioxide (CO2). In ideal gases, the system has a compressibility factor equal to one at any pressure, unlike real gases, where the compressibility factor can assume values smaller or larger than unity. To achieve this, a logical algorithm was developed for evaluating the compressibility factor using the Peng-Robinson (P-R) and Soave-Redlich-Kwong cubic equations of state, with mathematical resolution carried out using the Microsoft EXCEL SOLVER. The calculation procedure involved transforming the initial equations into cubic equations through linearization, followed by the calculation of compressibility factors that determine the phenomena associated with molecular attraction and repulsion within the referenced gas mixtures for different compositions, temperatures, and within a specific pressure range. The results of this analysis revealed the predominance of attractive and repulsive forces within the studied pressure range, with the transition occurring in the pressure range of 400 to 450 atm for both mathematical equations under evaluation. Furthermore, these attraction and repulsion phenomena are strongly influenced by the proportion of each gas in the mixture and the operating temperature. Therefore, understanding these phenomena enhances the scientific understanding of industrial processes involving phase equilibrium, especially when implemented in separation operations.