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Supercritical CO2 (S-CO2) cycles have found applications in power generation and can achieve high efficiency in a wide range of temperatures and pressures. The Redlich-Kwong-Aungier real gas equation of state is used to describe the thermodynamic properties of the CO2 working fluid. The main problem in its application lies in modeling the phase transition between different states and the region near the critical point of the working fluid. The object of the study is the working process in a centrifugal compressor located in the compression loop with the CO2 working fluid. The proposed mathematical model of the modified Redlich-Kwong-Aungier equation of state allows for a first-order phase transition from the liquid to the supercritical region even near the critical point. A scaling factor was added to the modified equation of state, significantly reducing the error in pressure determination in a wide range of temperatures compared to the original equation of state. The proposed mathematical model can be applied in the pure liquid region, limited to the temperature range from 220 K to 300 K. The mathematical model was used to solve the 3D gasdynamic problem, specifically to determine the thermodynamic and kinematic properties of the flow in a centrifugal compressor in a wide range of operating modes. A comparison of the calculation results with experimental data from the Sandia National Laboratories (USA) report was conducted. A satisfactory agreement of the results at the design point of the compressor characteristic was obtained (less than 5 % discrepancy). Due to the simplicity of the equation of state and the small number (seven) of empirical coefficients, the obtained mathematical model can be used for practical CFD tasks without significant computational time costs. [ABSTRACT FROM AUTHOR]