A combined experimental and simulation study for the separation of carbon dioxide and methane mixtures using NH2-MIL-53(Al) as adsorbent is presented. A fixed-bed model has been applied to simulate binary breakthrough experiments obtained in small lab-scale equipment (10 cm column, 1/4″ in diameter, 800 mg sample). A mixed Langmuir/Langmuir–Freundlich isotherm is used to capture the temperature dependence of the two-step isotherm and a linear driving force model to capture diffusion in the MOF crystals. The model is able to describe the experimental breakthrough data at 273 K over a pressure range of 1 to 20 bar. Displacement of methane by carbon dioxide, a large apparent roll-up effect, heats of adsorption and dispersion phenomena have been quantified taking into account post-column volumes often present in lab-scale equipment. The heat effects result in a maximum local temperature rise up to 20 K.