A Virial Equation of State for CO2 Mixtures for Turbomachinery Design and Analysis

Abstract In most industrial applications CO2 is produced with varying levels of component concentrations that have substantially varying volatilities. This presents a challenge for the equation of state to produce accurate thermodynamic predictions especially in the multi-phase regions. This challenge is accentuated in mixtures with combined polar and non-polar components. Highly accurate equation of states explicit in the Helmholtz free energy exist for various pure substances including pure CO2. These equations-of-state have been extended to CO2 mixtures with highly non-polar components, e.g. hydrocarbons, H2, and N2. However, due to the very high number of independent coefficients, the complexity of the equations, and the presence of relatively high concentration of polar components, e.g. water, in the mixture, these types of equations-of-state have not been widely adopted for industrial applications. This article presents a virial equation of state based on the modified Benedict-Webb-Rubin formulation by Bender applied to a general real gas mixture comprised of both polar and nonpolar components. A modified gas-liquid fugacity-based equilibrium formulation is also developed to be able to apply the Bender equation for general CO2 mixtures. The developed formulations are more robust and less numerically taxing than the more complicated Helmholtz free energy-based equations. This makes the developed equation of state especially useful during the typically iterative process involved in the turbomachinery equipment thermodynamic design. In this work details of the equation of state and the developed two-phase formulation are presented. Comparison with existing equations of state on a pure substance basis and mixture basis are presented. The developed method is used to design a prototype supercritical CO2 radial compressor stage. Comparisons with experimental measurements of the prototype stage using pure CO2 as well as CO2-N2 mixtures are presented both at subcritical and supercritical conditions. The developed equation of state predictions show high level of agreement with both the highly accurate Helmholtz free energy-based equations of state as well as the experimentally measured thermodynamic properties from the test article. The developed equation of state is therefore demonstrated to be suitable for the design and analysis of turbomachinery equipment.