Abstract Reforming of fossil fuels coupled with carbon capture and storage has the potential to produce low-carbon H2 at large scale and low cost. Adsorption is a potentially promising technology for two key separation tasks in this process: H2 purification and CO2 capture. In this work, we present equilibrium adsorption data of H2 and CH4 on zeolite 13X, in addition to the already established CO2 isotherms. Further, we carry out binary (CO2–CH4) and ternary (H2–CO2–CH4) breakthrough experiments at various pressures and temperatures to estimate transport parameters, assess the predictive capacity of our 1D column model, and compare different multi-component adsorption models. CO2 adsorbs strongly on zeolite 13X, CH4 adsorbs less, and H2 adsorbs very little. Thus, H2 breaks through first, CH4 second (first in the binary breakthrough experiments) and CO2 last. Linear driving force (LDF) mass transfer coefficients are estimated based on a single breakthrough experiment and mass transfer is found to be fast for H2, slower for CH4, and slowest for CO2. The LDF parameters can be used in a predictive manner for breakthrough experiments at varying pressures, temperatures, flows, and, though with lower accuracy, even compositions. Heat transfer inside the column is described well with a literature correlation, thus yielding an excellent agreement between simulated and measured column temperatures. Ideal and real adsorbed solution theories (IAST and RAST, respectively) both model the observed breakthrough composition profiles well, whereas extended isotherms are inferior for predicting the competitive behavior between CH4 and CO2 adsorption. This study provides the groundwork necessary for full cyclic experiments and their simulation.