The gas solubility in polymeric membranes affects the separation performance, particularly in the case of CO2 capture processes. Solubility and solubility-selectivity in membranes of multicomponent mixtures can deviate rather markedly from the corresponding pure gas values, due to swelling and competition phenomena, and require dedicated time-consuming measurements. Many experiments can be avoided by using a suitable thermodynamic tool, such as an Equation of State (EoS) model, to represent the gases sorption in the membrane. Such models require, for parameterization, knowledge of the polymer behavior above the glass transition Tg, which is a limit for membrane modeling, because the most attractive polymers for gas separation are rigid matrices characterized by very high Tg values, difficult to reach experimentally. In this work, we study the sorption of CO2/CH4 mixtures in a high-Tg polyimide membrane (Matrimid®) using a bottom-up approach. Pressure-volume-temperature data for Matrimid® above Tg are generated using NPT Molecular Dynamics simulations: the results are regressed to find Matrimid® parameters for the PC-SAFT Equation of State. Finally, the Non Equilibrium PC-SAFT macroscopic model (NE-PC-SAFT) is used to calculate CO2 and CH4 solubility and solubility-selectivity as a function of gas mixture pressure, composition and temperature. The approach is tested successfully over many experimental pure gas and vapor sorption data in Matrimid®. Mixed gas calculations predict a marked competition, which affects more methane than CO2 sorption, and results in a higher-than-ideal value of solubility-selectivity. Combined with the fact that experimental mixed gas permeability-selectivity is lower than the ideal value, such results indicate that the diffusivity of CH4 in Matrimid® is significantly enhanced in presence of CO2, causing a decrease of diffusivity-selectivity.