[Display omitted] • Synchrotron X-ray diffraction computed tomography applied to three packed bed catalytic membrane reactors. • The solid-state evolution of catalysts and membranes is tracked under operating conditions. • A new crystal structure model of BaCo 0.4 Fe 0.4 Zr 0.2 O 3- δ (BCFZ) is suggested and used for the diffraction data analysis. Catalytic membrane reactors have the potential to render the process of oxidative coupling of methane economically viable. Here, the results from operando XRD-CT studies of three different catalytic membrane reactors, employing BaCo 0.4 Fe 0.4 Zr 0.2 O 3-δ (BCFZ) and La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF) perovskite membranes with Mn-Na-W/SiO 2 and La-promoted Mn-Na-W/SiO 2 catalysts, are presented. It is shown that synchrotron X-ray tomographic diffraction imaging allows the extraction of spatially-resolved diffraction information from the interior of these working catalytic membrane reactors and makes it possible to capture the evolving solid-state chemistry of their components under various operating conditions (i.e. temperature and chemical environment). [ABSTRACT FROM AUTHOR]