The methanation of carbon dioxide has gained renewed interest during the last years as a possible technology to synthesize a feasible chemical energy carrier. This modeling study aims at a basic understanding of the aspects relevant for designing an externally cooled fixed-bed reactor for the methanation of a pure, stoichiometric feed gas. It is shown that the reaction rates and the exothermicity (Delta H degrees = -165 kJ/mol) prevent a fixed-bed reactor of technical dimensions to be operated at high conversions without runaway of the reactor. The model predictions of differently detailed pseudo-homogeneous reactor models and a heterogeneous reactor model where the intraparticle transport of mass is described according to a dusty-gas approach are compared to assess the needed level of detail in terms of modeling the heat transfer, fluid flow characteristics and transport resistances on the pellet scale. Under specific conditions, intraparticle mass transfer and external heat transfer need to be considered for describing the temperature and concentration profiles adequately. The study is completed by modeling a fixed-bed membrane reactor as an example of a structured reactor that offers improved temperature control by separated and controlled feeding. of hydrogen and carbon dioxide. (C) 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.