A detailed model is developed for the separation of strongly adsorbing gas mixtures at semi-pilot scale. It assumes a non-isothermal compressible transport-diffusion mechanism in the adsorber and dispersed compressible flow in the periphery, respectively. A methodology is proposed for efficient system analysis and parameter determination, leading to high model accuracy. The separation of N-2 and CO2 on the carbon molecular sieve CMS-H2 55/2 serves as example problem. Based on experimental equilibrium data for different temperatures, the applicability of different adsorption isotherm models is investigated for the single components. Isosteric heats of adsorption and their dependency on adsorbate loadings are determined by an analysis using the virial isotherm. A single reference experiment - an adsorption-desorption breakthrough for a diluted gas mixture - allows estimating heat and mass transfer coefficients and investigating the role of competitive adsorption and heat effects. The final model accurately predicts compositions, temperatures, and flow rates for a complete set of adsorption and desorption experiments in a broad range of conditions.