Cryogenic carbon dioxide removal from natural gas requires accurate thermodynamic phase study of the natural gas mixture and individual components. Thermodynamic data generation of carbon dioxide-methane mixture having 90 carbon dioxide for cryogenic carbon dioxide capture from natural gas using Peng Robinson equation of state is discussed in this research work. Golden section search technique along with Eureqa optimizing tool is then used to optimize the pressure-temperature conditions for the cryogenic carbon dioxide capture in the solid-vapour two-phase region. Cost optimization is done for the carbon dioxide capture system at atmospheric pressure and 20 bar. Temperature ranges for optimization were obtained from the predicted thermodynamic data for the mixture. The optimum temperatures obtained in this research work for the cryogenic carbon dioxide capture at atmospheric pressure and the 20 bar are �103.8 °C and �60.90 °C respectively. For atmospheric pressure at �103.8 °C the worth of methane, carbon dioxide, and energy is 114 /h, 9 /h, and 53 /h respectively, while at 20 bar and �60.9 °C the worth of carbon dioxide, methane, and the energy are found to be 129 /h, 46 /h, 52 /h, respectively. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim